Trellis coded modulation (TCM), introduced in 1982, is a combined channel coding and modulation technique. TCM improved coding gain, relative to existing techniques, without sacrificing either rate or the bandwidth. In the late 1980's, the original 2-dimensional (2D) TCM code was generalized to multidimensional modulations, offering a better trade-off between coding gain and complexity. However, these techniques cannot reach coding gains of 5-6 dB without excessive decoding complexity. In B. Li, A. Deczky, and A. Ginesi, “A new turbo coded QAM scheme with very low decoding complexity,” Global Telecommunications Conference, vol. 1, pp. 349-353, November 2001, the authors proposed a multilevel TCM code with reduced complexity. However, the proposed scheme concatenates several constituent codes with similar error-correcting capabilities and thus does not significantly improve coding gain.
Asymmetric Digital Subscriber Lines (ADSL) is a broadband technology for transmitting digital information at high speeds on the existing Public Switch Telephone Network (PSTN). The system is based on the Discrete Multitone (DMT) technique that divides the bandwidth in up to 256 orthogonal frequency subcarriers (tones) able to transmit independently from 2 to 15 bits/s/Hz, with 2-dimensional (2D) Quadrature Amplitude Modulation (QAM) constellations, optimized according to the SNR in each frequency band for a Bit Error Rate (BER) of 10−7. To further improve the “bit loading” of each tone, the G.992.1 International Telecommunication Union (ITU) standard recommends a coding chain formed by the serial concatenation of a Reed-Solomon (RS) code and a Trellis Coded Modulation (TCM) separated by an interleaver. Two modes are distinguished: 1) a fast mode without the interleaver and 2) a long latency mode, with interleaving, that allows a higher coding gain while increasing the transmission delay. The standard suggests using Wei's 16-state 4D TCM code as the inner code. See L. F. Wei, “Trellis-coded modulation with multidimensional constellations,” IEEE Trans. Inform. Theory, vol. 33, no. 4, pp. 483-501, July 1987.
Several unsuccessful attempts have been made to standardize an enhanced inner code for ADSL based on Turbo Trellis Coded Modulations (TTCM). Some schemes encoding two bits per tone achieve a coding gain of up to 6.8 dB (with RS code) for a BER of 10−7 (e.g., the B. Li, A. Deczky, and A. Ginesi scheme cited above or that of L. Zhang and A. Yongacoglu, “Turbo coding for transmission over ADSL,” Communication Technology Proceedings, WCC ICCT 2000, vol. 1, pp. 124-131, August 2000). However, the inherent high complexity of such schemes prevented the ASDL standardization committee from further considering these options as realistic better alternatives to the TCM scheme.